Venn Diagram Worksheet for Maths Olympiad

Maths Olympiad topic 32: Venn diagrams and inclusion–exclusion · Set 212 · 40 questions

How to solve it (Do not count twice): n(A or B) = n(A) + n(B) − n(both) — otherwise the “both” group is counted twice. Only A = n(A) − n(both). Neither = total − n(A or B). Both = n(A) + n(B) − n(A or B).

1. 1.In a class of 54 children, 25 like cricket, 25 like football and 6 like both. How many like neither? (a) 10 (b) 4 (c) 6 (d) 16
2. 2.In a class of 52 children, 28 like mangoes, 28 like bananas and 8 like both. How many like at least one of the two? (a) 40 (b) 48 (c) 56 (d) 52
3. 3.In a class of 20 children, 13 like cricket, 11 like football and 5 like both. How many like at least one of the two? (a) 20 (b) 24 (c) 19 (d) 14
4. 4.In a class of 34 children, 22 like tea, 13 like coffee and 5 like both. How many like only tea? (a) 21 (b) 22 (c) 17 (d) 8
5. 5.In a class of 16 children, 5 like maths, 12 like science and 2 like both. How many like neither? (a) 0 (b) 2 (c) 3 (d) 1
6. 6.In a class of 37 children, 22 like mangoes, 15 like bananas and 4 like neither. How many like both? (a) 4 (b) 5 (c) 3 (d) 33
7. 7.In a class of 45 children, 23 like maths, 18 like science and 7 like neither. How many like both? (a) 38 (b) 7 (c) 4 (d) 3
8. 8.In a class of 38 children, 24 like maths, 12 like science and 6 like neither. How many like both? (a) 4 (b) 32 (c) 5 (d) 6
9. 9.In a class of 39 children, 12 like mangoes, 26 like bananas and 9 like both. How many like neither? (a) 19 (b) 9 (c) 1 (d) 10
10. 10.In a class of 30 children, 7 like dance, 17 like music and 2 like both. How many like only dance? (a) 15 (b) 13 (c) 5 (d) 7
11. 11.In a class of 48 children, 28 like tea, 22 like coffee and 7 like neither. How many like both? (a) 7 (b) 2 (c) 41 (d) 9
12. 12.In a class of 45 children, 17 like mangoes, 27 like bananas and 9 like both. How many like neither? (a) 1 (b) 9 (c) 19 (d) 10
13. 13.In a class of 22 children, 14 like cricket, 11 like football and 7 like both. How many like only cricket? (a) 11 (b) 4 (c) 14 (d) 7
14. 14.In a class of 23 children, 15 like mangoes, 9 like bananas and 2 like both. How many like only mangoes? (a) 13 (b) 7 (c) 14 (d) 15
15. 15.In a class of 30 children, 10 like tea, 16 like coffee and 2 like both. How many like only tea? (a) 8 (b) 14 (c) 2 (d) 10
16. 16.In a class of 29 children, 11 like cricket, 19 like football and 1 like neither. How many like both? (a) 3 (b) 1 (c) 28 (d) 2
17. 17.In a class of 34 children, 27 like tea, 10 like coffee and 7 like both. How many like only tea? (a) 24 (b) 27 (c) 3 (d) 20
18. 18.In a class of 42 children, 20 like tea, 28 like coffee and 6 like neither. How many like both? (a) 12 (b) 36 (c) 13 (d) 6
19. 19.In a class of 41 children, 20 like dance, 23 like music and 5 like neither. How many like both? (a) 2 (b) 5 (c) 36 (d) 7
20. 20.In a class of 39 children, 18 like cricket, 22 like football and 2 like both. How many like at least one of the two? (a) 40 (b) 38 (c) 36 (d) 39
21. 21.In a class of 29 children, 12 like maths, 16 like science and 2 like both. How many like neither? (a) 1 (b) 5 (c) 3 (d) 2
22. 22.In a class of 32 children, 24 like cricket, 9 like football and 6 like both. How many like at least one of the two? (a) 32 (b) 21 (c) 27 (d) 33
23. 23.In a class of 41 children, 17 like dance, 21 like music and 6 like both. How many like only dance? (a) 15 (b) 17 (c) 11 (d) 20
24. 24.In a class of 30 children, 15 like maths, 8 like science and 3 like both. How many like neither? (a) 7 (b) 3 (c) 13 (d) 10
25. 25.In a class of 28 children, 5 like cricket, 18 like football and 7 like neither. How many like both? (a) 21 (b) 7 (c) 2 (d) 3
26. 26.In a class of 37 children, 19 like mangoes, 16 like bananas and 2 like both. How many like at least one of the two? (a) 35 (b) 31 (c) 33 (d) 37
27. 27.In a class of 39 children, 18 like mangoes, 30 like bananas and 10 like both. How many like only mangoes? (a) 20 (b) 18 (c) 9 (d) 8
28. 28.In a class of 43 children, 27 like maths, 26 like science and 1 like neither. How many like both? (a) 42 (b) 1 (c) 11 (d) 10
29. 29.In a class of 28 children, 22 like dance, 8 like music and 1 like neither. How many like both? (a) 2 (b) 1 (c) 27 (d) 3
30. 30.In a class of 42 children, 17 like cricket, 21 like football and 6 like neither. How many like both? (a) 36 (b) 3 (c) 2 (d) 6
31. 31.In a class of 15 children, 9 like cricket, 7 like football and 2 like neither. How many like both? (a) 13 (b) 3 (c) 2 (d) 1
32. 32.In a class of 21 children, 13 like maths, 10 like science and 4 like both. How many like at least one of the two? (a) 23 (b) 19 (c) 21 (d) 15
33. 33.In a class of 34 children, 26 like dance, 12 like music and 8 like both. How many like only dance? (a) 18 (b) 4 (c) 26 (d) 22
34. 34.In a class of 27 children, 14 like cricket, 14 like football and 2 like both. How many like only cricket? (a) 2 (b) 12 (c) 13 (d) 14
35. 35.In a class of 42 children, 21 like cricket, 19 like football and 3 like both. How many like at least one of the two? (a) 40 (b) 34 (c) 42 (d) 37
36. 36.In a class of 54 children, 30 like tea, 30 like coffee and 12 like both. How many like neither? (a) 12 (b) 6 (c) 18 (d) 7
37. 37.In a class of 38 children, 17 like dance, 24 like music and 7 like neither. How many like both? (a) 10 (b) 3 (c) 7 (d) 31
38. 38.In a class of 36 children, 22 like dance, 14 like music and 10 like neither. How many like both? (a) 10 (b) 11 (c) 26 (d) 9
39. 39.In a class of 21 children, 6 like dance, 9 like music and 3 like both. How many like only dance? (a) 3 (b) 6 (c) 4 (d) 12
40. 40.In a class of 35 children, 8 like tea, 19 like coffee and 2 like both. How many like at least one of the two? (a) 35 (b) 27 (c) 23 (d) 25

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